Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 88.5% → 98.6%

Time: 5.5s

Alternatives: 8

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))

C

double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) / (1.0d0 - (y / z))
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

function code(x, y, z)
	return Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) / (1.0 - (y / z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-255} \lor \neg \left(t\_0 \leq 5 \cdot 10^{-239}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-255) (not (<= t_0 5e-239)))
     t_0
     (- (/ (* x (- z)) y) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-255) || !(t_0 <= 5e-239)) {
		tmp = t_0;
	} else {
		tmp = ((x * -z) / y) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-255)) .or. (.not. (t_0 <= 5d-239))) then
        tmp = t_0
    else
        tmp = ((x * -z) / y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-255) || !(t_0 <= 5e-239)) {
		tmp = t_0;
	} else {
		tmp = ((x * -z) / y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-255) or not (t_0 <= 5e-239):
		tmp = t_0
	else:
		tmp = ((x * -z) / y) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-255) || !(t_0 <= 5e-239))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x * Float64(-z)) / y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-255) || ~((t_0 <= 5e-239)))
		tmp = t_0;
	else
		tmp = ((x * -z) / y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-255], N[Not[LessEqual[t$95$0, 5e-239]], $MachinePrecision]], t$95$0, N[(N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -2e-255 or 5e-239 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   if -2e-255 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 5e-239

   1. Initial program 15.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 97.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 97.3%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 99.8%

         \[\leadsto -\color{blue}{\frac{z}{\frac{y}{x + y}}} \]

      3. distribute-neg-frac 99.8%

         \[\leadsto \color{blue}{\frac{-z}{\frac{y}{x + y}}} \]

      4. +-commutative 99.8%

         \[\leadsto \frac{-z}{\frac{y}{\color{blue}{y + x}}} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{-z}{\frac{y}{y + x}}} \]

   6. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)} \]

      2. associate-*r/ 79.7%

         \[\leadsto -1 \cdot z + \left(-\color{blue}{x \cdot \frac{z}{y}}\right) \]

      3. unsub-neg 79.7%

         \[\leadsto \color{blue}{-1 \cdot z - x \cdot \frac{z}{y}} \]

      4. mul-1-neg 79.7%

         \[\leadsto \color{blue}{\left(-z\right)} - x \cdot \frac{z}{y} \]

      5. associate-*r/ 100.0%

         \[\leadsto \left(-z\right) - \color{blue}{\frac{x \cdot z}{y}} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\left(-z\right) - \frac{x \cdot z}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-255} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 5 \cdot 10^{-239}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - \frac{y}{z}}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-110}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 (/ y z)))))
   (if (<= y -2.8e+49)
     (- z)
     (if (<= y -1.3e-13)
       (+ x y)
       (if (<= y -4.2e-110)
         t_0
         (if (<= y 5.4e-115) (+ x y) (if (<= y 5e+91) t_0 (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.8e+49) {
		tmp = -z;
	} else if (y <= -1.3e-13) {
		tmp = x + y;
	} else if (y <= -4.2e-110) {
		tmp = t_0;
	} else if (y <= 5.4e-115) {
		tmp = x + y;
	} else if (y <= 5e+91) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - (y / z))
    if (y <= (-2.8d+49)) then
        tmp = -z
    else if (y <= (-1.3d-13)) then
        tmp = x + y
    else if (y <= (-4.2d-110)) then
        tmp = t_0
    else if (y <= 5.4d-115) then
        tmp = x + y
    else if (y <= 5d+91) then
        tmp = t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (1.0 - (y / z));
	double tmp;
	if (y <= -2.8e+49) {
		tmp = -z;
	} else if (y <= -1.3e-13) {
		tmp = x + y;
	} else if (y <= -4.2e-110) {
		tmp = t_0;
	} else if (y <= 5.4e-115) {
		tmp = x + y;
	} else if (y <= 5e+91) {
		tmp = t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (1.0 - (y / z))
	tmp = 0
	if y <= -2.8e+49:
		tmp = -z
	elif y <= -1.3e-13:
		tmp = x + y
	elif y <= -4.2e-110:
		tmp = t_0
	elif y <= 5.4e-115:
		tmp = x + y
	elif y <= 5e+91:
		tmp = t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (y <= -2.8e+49)
		tmp = Float64(-z);
	elseif (y <= -1.3e-13)
		tmp = Float64(x + y);
	elseif (y <= -4.2e-110)
		tmp = t_0;
	elseif (y <= 5.4e-115)
		tmp = Float64(x + y);
	elseif (y <= 5e+91)
		tmp = t_0;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (1.0 - (y / z));
	tmp = 0.0;
	if (y <= -2.8e+49)
		tmp = -z;
	elseif (y <= -1.3e-13)
		tmp = x + y;
	elseif (y <= -4.2e-110)
		tmp = t_0;
	elseif (y <= 5.4e-115)
		tmp = x + y;
	elseif (y <= 5e+91)
		tmp = t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+49], (-z), If[LessEqual[y, -1.3e-13], N[(x + y), $MachinePrecision], If[LessEqual[y, -4.2e-110], t$95$0, If[LessEqual[y, 5.4e-115], N[(x + y), $MachinePrecision], If[LessEqual[y, 5e+91], t$95$0, (-z)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e49 or 5.0000000000000002e91 < y

   1. Initial program 65.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.2%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.2%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 68.2%

      \[\leadsto \color{blue}{-z} \]

   if -2.7999999999999998e49 < y < -1.3e-13 or -4.20000000000000004e-110 < y < 5.4e-115

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 90.7%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 90.7%

      \[\leadsto \color{blue}{y + x} \]

   if -1.3e-13 < y < -4.20000000000000004e-110 or 5.4e-115 < y < 5.0000000000000002e91

   1. Initial program 98.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.2%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-115}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-28} \lor \neg \left(z \leq 7.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.06e+185)
   (+ x y)
   (if (<= z -7.5e+89)
     (/ y (- 1.0 (/ y z)))
     (if (or (<= z -1e-28) (not (<= z 7.5e-8)))
       (+ x y)
       (- (/ (* x (- z)) y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.06e+185) {
		tmp = x + y;
	} else if (z <= -7.5e+89) {
		tmp = y / (1.0 - (y / z));
	} else if ((z <= -1e-28) || !(z <= 7.5e-8)) {
		tmp = x + y;
	} else {
		tmp = ((x * -z) / y) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.06d+185)) then
        tmp = x + y
    else if (z <= (-7.5d+89)) then
        tmp = y / (1.0d0 - (y / z))
    else if ((z <= (-1d-28)) .or. (.not. (z <= 7.5d-8))) then
        tmp = x + y
    else
        tmp = ((x * -z) / y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.06e+185) {
		tmp = x + y;
	} else if (z <= -7.5e+89) {
		tmp = y / (1.0 - (y / z));
	} else if ((z <= -1e-28) || !(z <= 7.5e-8)) {
		tmp = x + y;
	} else {
		tmp = ((x * -z) / y) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.06e+185:
		tmp = x + y
	elif z <= -7.5e+89:
		tmp = y / (1.0 - (y / z))
	elif (z <= -1e-28) or not (z <= 7.5e-8):
		tmp = x + y
	else:
		tmp = ((x * -z) / y) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.06e+185)
		tmp = Float64(x + y);
	elseif (z <= -7.5e+89)
		tmp = Float64(y / Float64(1.0 - Float64(y / z)));
	elseif ((z <= -1e-28) || !(z <= 7.5e-8))
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(Float64(x * Float64(-z)) / y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.06e+185)
		tmp = x + y;
	elseif (z <= -7.5e+89)
		tmp = y / (1.0 - (y / z));
	elseif ((z <= -1e-28) || ~((z <= 7.5e-8)))
		tmp = x + y;
	else
		tmp = ((x * -z) / y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.06e+185], N[(x + y), $MachinePrecision], If[LessEqual[z, -7.5e+89], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1e-28], N[Not[LessEqual[z, 7.5e-8]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06000000000000004e185 or -7.49999999999999947e89 < z < -9.99999999999999971e-29 or 7.4999999999999997e-8 < z

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 86.1%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 86.1%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 86.1%

      \[\leadsto \color{blue}{y + x} \]

   if -1.06000000000000004e185 < z < -7.49999999999999947e89

   1. Initial program 99.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.1%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]

   if -9.99999999999999971e-29 < z < 7.4999999999999997e-8

   1. Initial program 74.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(x + y\right)}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 77.7%

         \[\leadsto \color{blue}{-\frac{z \cdot \left(x + y\right)}{y}} \]

      2. associate-/l* 76.4%

         \[\leadsto -\color{blue}{\frac{z}{\frac{y}{x + y}}} \]

      3. distribute-neg-frac 76.4%

         \[\leadsto \color{blue}{\frac{-z}{\frac{y}{x + y}}} \]

      4. +-commutative 76.4%

         \[\leadsto \frac{-z}{\frac{y}{\color{blue}{y + x}}} \]

   5. Simplified 76.4%

      \[\leadsto \color{blue}{\frac{-z}{\frac{y}{y + x}}} \]

   6. Taylor expanded in y around 0 79.3%

      \[\leadsto \color{blue}{-1 \cdot z + -1 \cdot \frac{x \cdot z}{y}} \]
   7. Step-by-step derivation

      1. mul-1-neg 79.3%

         \[\leadsto -1 \cdot z + \color{blue}{\left(-\frac{x \cdot z}{y}\right)} \]

      2. associate-*r/ 73.3%

         \[\leadsto -1 \cdot z + \left(-\color{blue}{x \cdot \frac{z}{y}}\right) \]

      3. unsub-neg 73.3%

         \[\leadsto \color{blue}{-1 \cdot z - x \cdot \frac{z}{y}} \]

      4. mul-1-neg 73.3%

         \[\leadsto \color{blue}{\left(-z\right)} - x \cdot \frac{z}{y} \]

      5. associate-*r/ 79.3%

         \[\leadsto \left(-z\right) - \color{blue}{\frac{x \cdot z}{y}} \]

   8. Simplified 79.3%

      \[\leadsto \color{blue}{\left(-z\right) - \frac{x \cdot z}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+185}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-28} \lor \neg \left(z \leq 7.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{-79} \lor \neg \left(x \leq 112\right):\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (or (<= x -2.05e-79) (not (<= x 112.0))) (/ x t_0) (/ y t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if ((x <= -2.05e-79) || !(x <= 112.0)) {
		tmp = x / t_0;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if ((x <= (-2.05d-79)) .or. (.not. (x <= 112.0d0))) then
        tmp = x / t_0
    else
        tmp = y / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if ((x <= -2.05e-79) || !(x <= 112.0)) {
		tmp = x / t_0;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if (x <= -2.05e-79) or not (x <= 112.0):
		tmp = x / t_0
	else:
		tmp = y / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if ((x <= -2.05e-79) || !(x <= 112.0))
		tmp = Float64(x / t_0);
	else
		tmp = Float64(y / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if ((x <= -2.05e-79) || ~((x <= 112.0)))
		tmp = x / t_0;
	else
		tmp = y / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.05e-79], N[Not[LessEqual[x, 112.0]], $MachinePrecision]], N[(x / t$95$0), $MachinePrecision], N[(y / t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.04999999999999997e-79 or 112 < x

   1. Initial program 87.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.3%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]

   if -2.04999999999999997e-79 < x < 112

   1. Initial program 87.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-79} \lor \neg \left(x \leq 112\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+52} \lor \neg \left(y \leq 1.35 \cdot 10^{+108}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.65e+52) (not (<= y 1.35e+108))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e+52) || !(y <= 1.35e+108)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.65d+52)) .or. (.not. (y <= 1.35d+108))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e+52) || !(y <= 1.35e+108)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.65e+52) or not (y <= 1.35e+108):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.65e+52) || !(y <= 1.35e+108))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.65e+52) || ~((y <= 1.35e+108)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.65e+52], N[Not[LessEqual[y, 1.35e+108]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e52 or 1.35e108 < y

   1. Initial program 65.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.6%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.6%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 68.6%

      \[\leadsto \color{blue}{-z} \]

   if -1.65e52 < y < 1.35e108

   1. Initial program 99.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.2%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 71.2%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 71.2%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+52} \lor \neg \left(y \leq 1.35 \cdot 10^{+108}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+48} \lor \neg \left(y \leq 4.7 \cdot 10^{-26}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+48) (not (<= y 4.7e-26))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+48) || !(y <= 4.7e-26)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.4d+48)) .or. (.not. (y <= 4.7d-26))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+48) || !(y <= 4.7e-26)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+48) or not (y <= 4.7e-26):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+48) || !(y <= 4.7e-26))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+48) || ~((y <= 4.7e-26)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+48], N[Not[LessEqual[y, 4.7e-26]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -2.4000000000000001e48 or 4.69999999999999989e-26 < y

   1. Initial program 72.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.9%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 59.9%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 59.9%

      \[\leadsto \color{blue}{-z} \]

   if -2.4000000000000001e48 < y < 4.69999999999999989e-26

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 60.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+48} \lor \neg \left(y \leq 4.7 \cdot 10^{-26}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 40.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e-81) x (if (<= x 2.5e-144) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-81) {
		tmp = x;
	} else if (x <= 2.5e-144) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.2d-81)) then
        tmp = x
    else if (x <= 2.5d-144) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-81) {
		tmp = x;
	} else if (x <= 2.5e-144) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e-81:
		tmp = x
	elif x <= 2.5e-144:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e-81)
		tmp = x;
	elseif (x <= 2.5e-144)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e-81)
		tmp = x;
	elseif (x <= 2.5e-144)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e-81], x, If[LessEqual[x, 2.5e-144], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999998e-81 or 2.4999999999999999e-144 < x

   1. Initial program 87.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.0%

      \[\leadsto \color{blue}{x} \]

   if -4.1999999999999998e-81 < x < 2.4999999999999999e-144

   1. Initial program 87.6%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.6%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]

   4. Taylor expanded in y around 0 46.2%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-144}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.0% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 87.4%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 36.2%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 36.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024027 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))